This mathematician names the identity that n choose k equals the sum from i equals k to n of i minus 1 choose k minus 1. The statement that local extrema of functions have a vanishing first derivative is his theorem of stationary points. This mathematician used the method of descent to prove the n equals 4 case of one of his statements, and also stated that light rays travel to minimize the time taken, his principle of (*) least time. Another law named for him states that for any a coprime to a prime p, a to the quantity p minus 1 is congruent 
This mathematician names the identity that n choose k equals the sum from i equals k to n of i minus 1 choose k minus 1. The statement that local extrema of functions have a vanishing first derivative is his theorem of stationary points. This mathematician used the method of descent to prove the n equals 4 case of one of his statements, and also stated that light rays travel to minimize the time taken, his principle of (*) least time. Another law named for him states that for any a coprime to a prime p, a to the quantity p minus 1 is congruent to 1 mod p; that is his Little Theorem. For 10 points, identify this namesake of a theorem proven by Andrew Wiles, stating that for there are no integer solutions to x to the n plus y to the n equals z to the n for n greater than two—his namesake Last Theorem.
This mathematician names the identity that n choose k equals the sum from i equals k to n of i minus 1 choose k minus 1.
Pierre de {Fermat}